Covering Based Generalized Rough Fuzzy Set Model

Abstract

The extension of rough set is an important issue in rough set theory among which the covering based generalized rough set is vital. Concept approximation in covering approximation space (CAS) is a key issue for acquiring knowledge from it. Some researchers have done much on approximation of classical sets in covering approximation space. Some covering based generalized rough fuzzy set models have already been developed for approximation of fuzzy sets in covering approximation space. Unfortunately, there are limitations in these models. In this paper, a new covering based generalized rough fuzzy set model is proposed. It solves the problems of former models. Moreover, the lower and upper approximations in two different covering approximation spaces with partial order relation are studied, and the sufficient and necessary condition for generating the same covering based generalized rough fuzzy sets from two different covering approximation spaces is that these two coverings have the same reductions. In the end, the relationship of this new model with the models proposed by Wei and Xu is analyzed. Wei’s model and Xu’s model are proved to be two extremes of the new one, and they can be used in some special cases of unary covering. These results provide foundation for the application of covering based generalized rough fuzzy set models to fuzzy decisions.